Optimized aerodynamic profile for a turbine blade, in particular for a rotary wheel of a turbine

ABSTRACT

When cold and in the non-coated state, the aerodynamic profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y, Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point under consideration from a first reference plane P0 situated at the base of the nominal profile, and H is the height of said profile measured from the first reference plane to a second reference plane P1. The measurements D and H are taken radially relative to the axis of the turbine, while the X coordinate is measured in the axial direction of the turbine.

CROSS-REFERENCE TO RELATED APPLICATION

This patent application claims benefit under 35 U.S.C. § 119 to U.S.Provisional Patent Application No. 62/504,558, filed May 11, 2017, theentirety of which is incorporated herein by reference.

INTRODUCTION

The present disclosure relates to an aerodynamic profile for a turbineblade.

In particular, the disclosure relates to the aerodynamic profile of ablade of a rotary wheel of a gas turbine, and more particularly of a lowpressure turbine of the type used in a turbojet of an aircraft.

The disclosure relates in particular to a blade of the rotary wheel of aturbine having a plurality of stages, preferably five stages.

Such a profile should enable the turbine to provide the desiredefficiency, and in order to do that it must be such that the flow of airaround the profile is sound, i.e. substantially such that it does notgive rise to turbulence, which is harmful for overall efficiency.

It must be capable of being installed properly in the environment of theengine, and in particular, for the blade of a rotary wheel forming aportion of the rotor of the turbine, it must be capable of beingfastened easily to the support disk of the rotary wheel, via the root ofthe blade, whereas its tip must be capable of carrying a top platform.Furthermore, this part must present a profile enabling it to bemanufactured in a reliable and cost-effective manner by availablemanufacturing methods, such as casting, forging, machining, additivefabrication, or else weaving, without this list being limitative.

Furthermore, the profile of the blade must enable it to withstand themechanical stresses to which the blade is subjected, by enabling thosestresses to be spread over the entire blade in such a manner as to avoidpremature wear thereof. This spreading must apply both in static modeand in dynamic mode. In particular, it must be such that the blade,given its resonant modes, can withstand the highest dynamic loading forgood operation of the turbine.

An object of the disclosure is to propose an aerodynamic profile for aturbine blade that is optimized, and capable of satisfying thoseobjectives.

This object is achieved by the fact that when cold and in a non-coatedstate, said profile is substantially identical to a nominal profiledetermined by the Cartesian coordinates X,Y,Zadim given in Table 1, inwhich the coordinate Zadim is the quotient D/H where D is the distanceof the point P under consideration from a reference X,Y plane situatedat the base of the nominal profile, and H is the height of said profilemeasured from said reference plane that is the intersection of thestacking axis of the blade and the axisymmetric surface of the hub, outto a second reference plane that is the intersection of said stackingaxis with the axisymmetric surface of the casing, the measurements D andH being taken radially relative to the axis of the turbine, while thecoordinate X is measured in the axial direction of the turbine.

This profile has been determined as a result of numerous tests andsimulations. It is defined cold, i.e. at an ambient temperature of 20°C. That is a reference temperature at which the profile is geometricallydetermined. The above-mentioned objectives of aerodynamics andmechanical optimization are naturally valid for the conditions of use ofthis aerodynamic profile, i.e. when hot, at a temperature that isstabilized when the engine of which the turbine forms a part is beingused under cruising conditions.

Furthermore, the aerodynamic profile of the disclosure is defined in thenon-coated state. Since turbine blades are subjected to high temperaturegradients, it is common practice for them to be provided with a coatinghaving thermal properties enabling them more easily to withstand suchtemperature variations. The profile is determined prior to installingsuch a coating.

It is stated above that the profile of the disclosure is “substantiallyidentical” to the nominal profile. This means that the profile maydepart very slightly from said nominal profile.

The aerodynamic profile is thus preferably defined within an envelope of±1 millimeter (mm) in a direction normal to the surface of the nominalprofile.

-   -   It is also preferable for the X,Y coordinates of the aerodynamic        profile to lie within a range of ±5% relative to the X,Y        coordinates of the nominal profile.    -   In addition, the aerodynamic profile may be positioned rotated        within ±10°, particularly within ±5°, more particularly within        ±3°, with respect to the stacking axis.

These variations take account in particular of at least one ofmanufacturing tolerances of the profile, the setting of the profile toadapt to the flow coming from the turbine vanes situated upstream, andpossible deformation occurring when mounting the blade and integratingthe same in the rotary wheel. In particular, the profile is adapted soas to be optimized for the flow coming from the nozzle of the same stageof a turbine, when the blade of the disclosure belongs to a rotary wheelof a turbine.

For a blade of a rotary wheel, forming a portion of the rotor of aturbine, the profile serves to optimize the inter-blade flow, i.e. theflow between adjacent blades of the wheel, and thus transforms a maximumamount of the kinetic energy of the gaseous fluid into kinetic energy onthe shaft of the turbine. In addition, it serves to orient the gaseousfluid correctly for the turbine vanes situated downstream, in particularbelonging to the stationary nozzle of the next stage of the turbine, ifsuch a next stage exists.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure can be better understood and its advantages appear betteron reading the following detailed description of an embodiment given byway of non-limiting example. The description refers to the accompanyingdrawings, in which:

FIG. 1 is a fragmentary axial diagrammatic section view of a turbineincluding a blade of profile that corresponds to that of the disclosure;

FIG. 2 shows a blade of the turbine.

DETAILED DESCRIPTION

The turbine shown in axial section in FIG. 1 comprises five stagesreferenced respectively S1 to S5. In the direction DF going fromupstream to downstream, each stage comprises a nozzle that forms aportion of the stator of the turbine and that has a plurality ofradially-oriented vanes, and a rotary wheel that forms a portion of therotor of the turbine and that likewise includes a plurality ofradially-oriented blades.

In FIG. 1, the vanes of the nozzles of stages S1 to S5 are givenreferences N1 to N5 (these vanes are shown in dashed lines, for ease ofrepresentation), whereas the blades of rotary wheels of stages S1 to S5are given respective references W1 to W5.

In known manner, the vanes of the nozzles are fastened at both ends tostationary structure portions, while the blades of the rotary wheels arefastened to a rotary disk via their roots that are formed at theirradially-inner ends closer to the axis of the rotation A of the turbine.The disks forming parts of the wheels W1 to W5 are constrained to rotatetogether. The tips of the blades of the rotary wheels, formed at theirradially-outer ends, may carry top platforms.

The disclosure relates in particular to a blade of one of the rotarywheels of the turbine that, as mentioned above, preferably comprisesfive stages as shown, without this number being limiting.

The blade shown in FIG. 2 includes, at its radially-inner end, a bladeroot enabling it to be connected to a support disk forming the hub of aturbine wheel, and a platform 14 from which an aerodynamic profile 18extends. At its tip, formed at its radially-outer end remote from theplatform 14, the blade includes a top platform 10 that forms an outercasing carried by the various blades of the wheel.

By convention, the aerodynamic profile 18 is the entire portion of saidblade that extends radially from the platform 14 to the top platform 10.

In FIG. 2, there can be seen a frame of reference comprising Cartesiancoordinates X,Y,Z. The radial direction Z is the height direction of theblade, which extends radially from its root to its tip. This direction Zis perpendicular to the axial direction X which is the direction of theaxis of rotation A of the turbine. The direction Y is perpendicular tothe X,Z plane and is therefore tangential to the direction of rotationof the turbine.

The nominal profile from which the aerodynamic profile of the disclosureis determined is defined in following Table 1 of coordinates, in whichthe coordinates Zadim, measured along the axis Z is non-dimensional,whereas the dimensions X and Y, respectively measured along the axes Xand Y, are expressed in millimeters.

TABLE 1 X Y Zadim −8.75364 0.302241 −0.15 −8.77371 0.342368 −0.15−8.79671 0.40332 −0.15 −8.81967 0.501397 −0.15 −8.82357 0.641623 −0.15−8.78595 0.82035 −0.15 −8.69027 1.028424 −0.15 −8.52735 1.251364 −0.15−8.296 1.478957 −0.15 −7.99828 1.704459 −0.15 −7.63644 1.922326 −0.15−7.21279 2.127256 −0.15 −6.7303 2.314843 −0.15 −6.19215 2.480407 −0.15−5.602 2.618807 −0.15 −4.96336 2.720578 −0.15 −4.28131 2.777076 −0.15−3.56256 2.780458 −0.15 −2.81541 2.723985 −0.15 −2.04878 2.601886 −0.15−1.27312 2.4099 −0.15 −0.49956 2.145443 −0.15 0.261136 1.809619 −0.150.999543 1.407108 −0.15 1.708303 0.945512 −0.15 2.382974 0.435075 −0.153.020564 −0.11412 −0.15 3.618959 −0.69274 −0.15 4.178638 −1.29036 −0.154.701145 −1.8971 −0.15 5.187834 −2.50456 −0.15 5.638453 −3.10652 −0.156.0562 −3.69499 −0.15 6.442752 −4.26389 −0.15 6.798503 −4.80869 −0.157.124544 −5.32496 −0.15 7.422351 −5.80861 −0.15 7.692539 −6.25671 −0.157.935443 −6.66707 −0.15 8.151954 −7.03777 −0.15 8.342698 −7.36771 −0.158.508306 −7.65647 −0.15 8.649489 −7.90426 −0.15 8.767306 −8.1119 −0.158.862864 −8.28092 −0.15 8.933805 −8.41568 −0.15 8.936224 −8.52963 −0.158.903703 −8.60219 −0.15 8.871176 −8.64023 −0.15 8.84086 −8.6639 −0.158.811147 −8.6803 −0.15 8.769265 −8.69446 −0.15 8.699384 −8.69911 −0.158.60465 −8.66584 −0.15 8.519833 −8.56185 −0.15 8.423979 −8.41982 −0.158.305708 −8.24547 −0.15 8.163763 −8.03764 −0.15 7.99716 −7.79571 −0.157.804971 −7.51971 −0.15 7.586508 −7.2102 −0.15 7.340971 −6.86844 −0.157.068213 −6.49585 −0.15 6.767282 −6.09501 −0.15 6.437292 −5.66903 −0.156.077958 −5.22117 −0.15 5.688791 −4.75538 −0.15 5.268438 −4.27696 −0.154.816098 −3.79146 −0.15 4.332011 −3.30414 −0.15 3.815193 −2.82229 −0.153.265588 −2.35323 −0.15 2.68429 −1.90406 −0.15 2.07329 −1.48194 −0.151.435588 −1.09381 −0.15 0.775637 −0.7452 −0.15 0.099311 −0.43962 −0.15−0.58643 −0.17838 −0.15 −1.27458 0.038158 −0.15 −1.9584 0.21015 −0.15−2.63121 0.338994 −0.15 −3.28666 0.427038 −0.15 −3.9189 0.476932 −0.15−4.52263 0.491206 −0.15 −5.09305 0.473297 −0.15 −5.62586 0.427494 −0.15−6.11803 0.36099 −0.15 −6.56778 0.281482 −0.15 −6.97464 0.198406 −0.15−7.33912 0.120428 −0.15 −7.66236 0.056112 −0.15 −7.94573 0.013558 −0.15−8.18867 0.000391 −0.15 −8.38914 0.025465 −0.15 −8.54026 0.083339 −0.15−8.64049 0.155714 −0.15 −8.7005 0.221049 −0.15 −8.55475 0.492727 −0.07−8.57627 0.53363 −0.07 −8.60148 0.595828 −0.07 −8.62641 0.696509 −0.07−8.63229 0.841036 −0.07 −8.59603 1.025556 −0.07 −8.50041 1.241329 −0.07−8.33747 1.474472 −0.07 −8.10602 1.715698 −0.07 −7.8074 1.958293 −0.07−7.44319 2.196342 −0.07 −7.01515 2.42397 −0.07 −6.52537 2.634808 −0.07−5.97692 2.823241 −0.07 −5.37299 2.981751 −0.07 −4.71727 3.099526 −0.07−4.01539 3.16569 −0.07 −3.27497 3.170837 −0.07 −2.50576 3.105193 −0.07−1.71902 2.961615 −0.07 −0.92742 2.735842 −0.07 −0.14376 2.427385 −0.070.620426 2.040366 −0.07 1.355966 1.582612 −0.07 2.056467 1.064425 −0.072.718737 0.497888 −0.07 3.341338 −0.10538 −0.07 3.922425 −0.73604 −0.074.463846 −1.38284 −0.07 4.968059 −2.03569 −0.07 5.436697 −2.68636 −0.075.870132 −3.32839 −0.07 6.27142 −3.95423 −0.07 6.642504 −4.55786 −0.076.984044 −5.13463 −0.07 7.297076 −5.68024 −0.07 7.583089 −6.19071 −0.077.842733 −6.6631 −0.07 8.076332 −7.09526 −0.07 8.284696 −7.48536 −0.078.468408 −7.83234 −0.07 8.628035 −8.13584 −0.07 8.764228 −8.39617 −0.078.877947 −8.61424 −0.07 8.970238 −8.7917 −0.07 9.03917 −8.93262 −0.079.040807 −9.05003 −0.07 9.006861 −9.12459 −0.07 8.973033 −9.1635 −0.078.941491 −9.18748 −0.07 8.910601 −9.20376 −0.07 8.867125 −9.2171 −0.078.79511 −9.21866 −0.07 8.700534 −9.1772 −0.07 8.618603 −9.06618 −0.078.524976 −8.91684 −0.07 8.409612 −8.73339 −0.07 8.271364 −8.5145 −0.078.109367 −8.25942 −0.07 7.92287 −7.96803 −0.07 7.711294 −7.64076 −0.077.473996 −7.27871 −0.07 7.210864 −6.88326 −0.07 6.921177 −6.45673 −0.076.604049 −6.00213 −0.07 6.259278 −5.52253 −0.07 5.886292 −5.02181 −0.075.483597 −4.50509 −0.07 5.050401 −3.97757 −0.07 4.586503 −3.44459 −0.074.090798 −2.91297 −0.07 3.561785 −2.39086 −0.07 3.000606 −1.88478 −0.072.408558 −1.40203 −0.07 1.787302 −0.95054 −0.07 1.138944 −0.53921 −0.070.46935 −0.17251 −0.07 −0.2149 0.146177 −0.07 −0.90747 0.412695 −0.07−1.60105 0.624938 −0.07 −2.28781 0.782833 −0.07 −2.95995 0.887778 −0.07−3.61015 0.942462 −0.07 −4.23123 0.950996 −0.07 −4.81741 0.91877 −0.07−5.3636 0.852448 −0.07 −5.8662 0.760149 −0.07 −6.32327 0.651228 −0.07−6.73483 0.536788 −0.07 −7.10216 0.426961 −0.07 −7.42749 0.331445 −0.07−7.71344 0.260259 −0.07 −7.96134 0.223618 −0.07 −8.1688 0.22825 −0.07−8.32871 0.274992 −0.07 −8.43513 0.344612 −0.07 −8.49844 0.410308 −0.07−8.3797 −0.05122 0.00 −8.40614 −0.01162 0.00 −8.4388 0.049325 0.00−8.47459 0.149952 0.00 −8.49499 0.297667 0.00 −8.4761 0.490388 0.00−8.39958 0.721231 0.00 −8.25748 0.977459 0.00 −8.04807 1.250832 0.00−7.77152 1.534746 0.00 −7.42827 1.823004 0.00 −7.019 2.109209 0.00−6.54473 2.386357 0.00 −6.00669 2.645987 0.00 −5.40616 2.876464 0.00−4.74687 3.067235 0.00 −4.03391 3.205758 0.00 −3.27472 3.278115 0.00−2.47931 3.271587 0.00 −1.66093 3.176352 0.00 −0.83429 2.987334 0.00−0.01393 2.705092 0.00 0.787485 2.335799 0.00 1.560355 1.889541 0.002.298362 1.378635 0.00 2.998454 0.816556 0.00 3.659159 0.215689 0.004.279449 −0.41333 0.00 4.860679 −1.05927 0.00 5.404971 −1.71184 0.005.913827 −2.36256 0.00 6.387619 −3.0047 0.00 6.828559 −3.63091 0.007.238318 −4.23499 0.00 7.61739 −4.81217 0.00 7.966368 −5.35818 0.008.286384 −5.869 0.00 8.577867 −6.34166 0.00 8.840926 −6.77398 0.009.076136 −7.16417 0.00 9.283941 −7.51116 0.00 9.464802 −7.81462 0.009.619349 −8.07485 0.00 9.748523 −8.2928 0.00 9.853461 −8.47015 0.009.933045 −8.61079 0.00 9.944625 −8.73119 0.00 9.916108 −8.81062 0.009.884582 −8.85338 0.00 9.854044 −8.88047 0.00 9.823438 −8.89939 0.009.779548 −8.91581 0.00 9.705473 −8.92059 0.00 9.607496 −8.87923 0.009.518299 −8.76855 0.00 9.413351 −8.62028 0.00 9.284243 −8.43805 0.009.129823 −8.22047 0.00 8.949268 −7.96675 0.00 8.741979 −7.67667 0.008.507534 −7.35059 0.00 8.245539 −6.98953 0.00 7.956041 −6.5948 0.007.638735 −6.16858 0.00 7.293034 −5.71385 0.00 6.919095 −5.23354 0.006.516611 −4.73152 0.00 6.08441 −4.21287 0.00 5.622224 −3.68256 0.005.129926 −3.14601 0.00 4.606441 −2.61021 0.00 4.050837 −2.08292 0.003.464047 −1.57093 0.00 2.846846 −1.08223 0.00 2.200367 −0.62566 0.001.526994 −0.21011 0.00 0.831518 0.157681 0.00 0.119737 0.471444 0.00−0.60161 0.725422 0.00 −1.32441 0.915879 0.00 −2.03965 1.041545 0.00−2.73806 1.103543 0.00 −3.41053 1.105237 0.00 −4.0483 1.052405 0.00−4.64508 0.9527 0.00 −5.1954 0.816032 0.00 −5.69622 0.653198 0.00−6.14667 0.475615 0.00 −6.54844 0.29571 0.00 −6.90461 0.124693 0.00−7.21942 −0.02683 0.00 −7.49722 −0.1491 0.00 −7.74134 −0.23307 0.00−7.95244 −0.26709 0.00 −8.12282 −0.24664 0.00 −8.24098 −0.18989 0.00−8.31318 −0.12968 0.00 −8.12184 0.462074 0.10 −8.14853 0.503661 0.10−8.18111 0.567599 0.10 −8.216 0.672774 0.10 −8.23312 0.826652 0.10−8.20737 1.025939 0.10 −8.12136 1.263267 0.10 −7.96855 1.526132 0.10−7.7479 1.807261 0.10 −7.45934 2.100399 0.10 −7.10287 2.399292 0.10−6.67861 2.697036 0.10 −6.18685 2.985413 0.10 −5.62796 3.253879 0.10−5.00363 3.490374 0.10 −4.31737 3.681411 0.10 −3.57466 3.810544 0.10−2.78507 3.86062 0.10 −1.96057 3.816314 0.10 −1.11845 3.66731 0.10−0.27672 3.410452 0.10 0.548141 3.049585 0.10 1.343053 2.594884 0.102.099316 2.060182 0.10 2.812435 1.460813 0.10 3.481435 0.812247 0.104.106495 0.127872 0.10 4.688919 −0.58022 0.10 5.230916 −1.301 0.105.735611 −2.02425 0.10 6.205499 −2.74133 0.10 6.641819 −3.44529 0.107.046719 −4.12929 0.10 7.422354 −4.78717 0.10 7.769614 −5.41408 0.108.089119 −6.00587 0.10 8.382084 −6.55863 0.10 8.649043 −7.0694 0.108.890122 −7.53603 0.10 9.105837 −7.95679 0.10 9.296593 −8.33071 0.109.462764 −8.65753 0.10 9.604896 −8.93765 0.10 9.72378 −9.17219 0.109.820439 −9.36296 0.10 9.894296 −9.51353 0.10 9.902419 −9.63879 0.109.870271 −9.72026 0.10 9.836013 −9.76347 0.10 9.803174 −9.79024 0.109.770341 −9.8083 0.10 9.723673 −9.8225 0.10 9.646365 −9.82079 0.109.550298 −9.76606 0.10 9.466814 −9.6438 0.10 9.367643 −9.48274 0.109.245852 −9.28463 0.10 9.100478 −9.04788 0.10 8.930872 −8.77152 0.108.736654 −8.45512 0.10 8.517556 −8.09892 0.10 8.273374 −7.70376 0.108.004178 −7.27093 0.10 7.709907 −6.80239 0.10 7.389961 −6.30097 0.107.044546 −5.76953 0.10 6.673183 −5.21186 0.10 6.274422 −4.6329 0.105.847986 −4.03734 0.10 5.393137 −3.43069 0.10 4.907855 −2.82004 0.104.390827 −2.2127 0.10 3.841842 −1.61592 0.10 3.259912 −1.03856 0.102.644277 −0.49071 0.10 1.996331 0.018224 0.10 1.318845 0.478753 0.100.615622 0.880646 0.10 −0.10697 1.215245 0.10 −0.84038 1.475811 0.10−1.57422 1.658138 0.10 −2.29712 1.76172 0.10 −2.9967 1.789329 0.10−3.66162 1.74762 0.10 −4.28357 1.646579 0.10 −4.85522 1.498676 0.10−5.37313 1.318317 0.10 −5.83673 1.119976 0.10 −6.24781 0.917123 0.10−6.61052 0.722952 0.10 −6.93019 0.549324 0.10 −7.21138 0.405097 0.10−7.45925 0.301481 0.10 −7.67607 0.25017 0.10 −7.8541 0.260495 0.10−7.97881 0.316429 0.10 −8.05375 0.379398 0.10 −7.87412 0.624291 0.20−7.90242 0.666623 0.20 −7.93705 0.731964 0.20 −7.97445 0.839871 0.20−7.99307 0.998317 0.20 −7.96726 1.203824 0.20 −7.88032 1.448982 0.20−7.72655 1.721959 0.20 −7.50527 2.016351 0.20 −7.21597 2.326171 0.20−6.85874 2.645893 0.20 −6.43209 2.967293 0.20 −5.93527 3.280969 0.20−5.36868 3.576523 0.20 −4.73315 3.840143 0.20 −4.0313 4.055386 0.20−3.26827 4.201746 0.20 −2.45532 4.260016 0.20 −1.60564 4.212497 0.20−0.7398 4.048035 0.20 0.121604 3.764458 0.20 0.960498 3.368158 0.201.763811 2.872932 0.20 2.523697 2.29538 0.20 3.236724 1.652618 0.203.902937 0.961133 0.20 4.524139 0.235589 0.20 5.102155 −0.51181 0.205.63923 −1.27025 0.20 6.13891 −2.02941 0.20 6.60415 −2.78047 0.207.036439 −3.51638 0.20 7.437678 −4.23049 0.20 7.810218 −4.91655 0.208.155033 −5.56965 0.20 8.472632 −6.18564 0.20 8.764185 −6.76064 0.209.030183 −7.29166 0.20 9.270705 −7.77653 0.20 9.486162 −8.21357 0.209.676894 −8.60183 0.20 9.843205 −8.94108 0.20 9.985593 −9.23179 0.2010.10477 −9.47514 0.20 10.20173 −9.67306 0.20 10.27652 −9.82885 0.2010.28708 −9.95777 0.20 10.25531 −10.0422 0.20 10.22044 −10.0871 0.2010.18667 −10.1148 0.20 10.15252 −10.1332 0.20 10.10396 −10.147 0.2010.02395 −10.142 0.20 9.928182 −10.0796 0.20 9.844683 −9.95102 0.209.744135 −9.78296 0.20 9.620829 −9.57614 0.20 9.4739 −9.32885 0.209.302803 −9.03999 0.20 9.107325 −8.70902 0.20 8.887344 −8.33607 0.208.64283 −7.92191 0.20 8.373907 −7.46781 0.20 8.080791 −6.9756 0.207.763019 −6.44807 0.20 7.420852 −5.88807 0.20 7.053891 −5.29935 0.206.66062 −4.68687 0.20 6.240851 −4.05522 0.20 5.793706 −3.40994 0.205.316643 −2.75829 0.20 4.808282 −2.10747 0.20 4.267982 −1.46484 0.203.69381 −0.83977 0.20 3.084047 −0.24288 0.20 2.439085 0.315483 0.201.760575 0.824435 0.20 1.051421 1.27208 0.20 0.317036 1.646828 0.20−0.43402 1.938909 0.20 −1.19026 2.141537 0.20 −1.93828 2.252781 0.20−2.66271 2.275779 0.20 −3.35006 2.21877 0.20 −3.99049 2.094081 0.20−4.57566 1.916986 0.20 −5.10187 1.703565 0.20 −5.56904 1.470464 0.20−5.98087 1.234509 0.20 −6.34262 1.009645 0.20 −6.66023 0.807171 0.20−6.93933 0.636383 0.20 −7.18613 0.508173 0.20 −7.40477 0.434549 0.20−7.58919 0.428433 0.20 −7.72175 0.478 0.20 −7.80166 0.540355 0.20−7.61968 0.952715 0.30 −7.64828 0.996183 0.30 −7.68287 1.063362 0.30−7.72026 1.173926 0.30 −7.73727 1.336013 0.30 −7.70603 1.54536 0.30−7.61147 1.793765 0.30 −7.45043 2.070398 0.30 −7.2222 2.369572 0.30−6.9262 2.685741 0.30 −6.56119 3.01241 0.30 −6.12622 3.342296 0.30−5.62062 3.666331 0.30 −5.04345 3.971726 0.30 −4.39454 4.242171 0.30−3.67658 4.459358 0.30 −2.89568 4.602685 0.30 −2.0646 4.650903 0.30−1.1975 4.584679 0.30 −0.31777 4.39244 0.30 0.552102 4.073229 0.301.393563 3.636625 0.30 2.193878 3.098763 0.30 2.946117 2.478054 0.303.648047 1.792888 0.30 4.300916 1.06052 0.30 4.907729 0.296152 0.305.470877 −0.48799 0.30 5.992783 −1.28129 0.30 6.477444 −2.07341 0.306.928262 −2.8555 0.30 7.346783 −3.62057 0.30 7.73489 −4.36209 0.308.095162 −5.07377 0.30 8.42862 −5.7507 0.30 8.735771 −6.38876 0.309.017816 −6.98405 0.30 9.275246 −7.53358 0.30 9.508146 −8.03518 0.309.716887 −8.48718 0.30 9.901773 −8.88864 0.30 10.06309 −9.23937 0.3010.20126 −9.53988 0.30 10.31696 −9.79141 0.30 10.41114 −9.99596 0.3010.48416 −10.1567 0.30 10.49459 −10.2885 0.30 10.46198 −10.3747 0.3010.42607 −10.4204 0.30 10.39122 −10.4482 0.30 10.35577 −10.4665 0.3010.30552 −10.4791 0.30 10.22355 −10.4701 0.30 10.12915 −10.4007 0.3010.04738 −10.2661 0.30 9.948194 −10.0911 0.30 9.8267 −9.87572 0.309.682124 −9.61809 0.30 9.514023 −9.31704 0.30 9.322289 −8.97196 0.309.106936 −8.5829 0.30 8.868102 −8.15053 0.30 8.605815 −7.6762 0.308.320536 −7.16165 0.30 8.011933 −6.60956 0.30 7.680161 −6.02288 0.307.32492 −5.40531 0.30 6.9446 −4.76175 0.30 6.538937 −4.09683 0.306.107018 −3.416 0.30 5.645838 −2.72661 0.30 5.153752 −2.03581 0.304.629858 −1.35094 0.30 4.071352 −0.68168 0.30 3.475453 −0.03912 0.302.841764 0.565907 0.30 2.170891 1.121566 0.30 1.464389 1.6142 0.300.726892 2.030266 0.30 −0.03308 2.357999 0.30 −0.80327 2.588886 0.30−1.56893 2.719528 0.30 −2.31242 2.752773 0.30 −3.01848 2.697337 0.30−3.67575 2.566693 0.30 −4.27462 2.378064 0.30 −4.81141 2.15021 0.30−5.28614 1.900895 0.30 −5.70287 1.648028 0.30 −6.06762 1.406432 0.30−6.38712 1.188377 0.30 −6.66783 1.003612 0.30 −6.91552 0.86138 0.30−7.1358 0.77443 0.30 −7.32464 0.757668 0.30 −7.46252 0.803422 0.30−7.54544 0.866384 0.30 −7.38087 1.261058 0.40 −7.4094 1.305411 0.40−7.44355 1.373944 0.40 −7.47846 1.487065 0.40 −7.49031 1.651641 0.40−7.45266 1.863034 0.40 −7.35115 2.112406 0.40 −7.1827 2.389663 0.40−6.94729 2.689709 0.40 −6.64455 3.007597 0.40 −6.27262 3.336442 0.40−5.83079 3.669395 0.40 −5.31785 3.996861 0.40 −4.73258 4.305724 0.40−4.07485 4.579619 0.40 −3.34641 4.796953 0.40 −2.55377 4.936224 0.40−1.71127 4.974435 0.40 −0.83366 4.891974 0.40 0.053471 4.678267 0.400.927311 4.334293 0.40 1.769541 3.871877 0.40 2.568085 3.308378 0.403.316377 2.662472 0.40 4.012671 1.952834 0.40 4.658163 1.196414 0.405.256581 0.408822 0.40 5.810886 −0.39748 0.40 6.323899 −1.21176 0.406.800006 −2.02361 0.40 7.242857 −2.82419 0.40 7.653831 −3.60667 0.408.034902 −4.36449 0.40 8.38875 −5.09138 0.40 8.716324 −5.78246 0.409.018143 −6.43361 0.40 9.295404 −7.04092 0.40 9.548572 −7.60143 0.409.777712 −8.11294 0.40 9.983173 −8.57381 0.40 10.16523 −8.9831 0.4010.32413 −9.34064 0.40 10.46027 −9.64696 0.40 10.57433 −9.90334 0.4010.66718 −10.1118 0.40 10.73929 −10.2756 0.40 10.75001 −10.4092 0.4010.71725 −10.4966 0.40 10.68088 −10.543 0.40 10.64545 −10.571 0.4010.60913 −10.5893 0.40 10.55774 −10.6012 0.40 10.47438 −10.5897 0.4010.38079 −10.5157 0.40 10.29966 −10.3772 0.40 10.20078 −10.1977 0.4010.07976 −9.97664 0.40 9.935895 −9.71221 0.40 9.768808 −9.40313 0.409.578485 −9.04873 0.40 9.364985 −8.64904 0.40 9.128658 −8.20463 0.408.869467 −7.71691 0.40 8.587932 −7.1876 0.40 8.284 −6.61925 0.407.957641 −6.01495 0.40 7.608689 −5.37831 0.40 7.235558 −4.71422 0.406.837791 −4.02738 0.40 6.41457 −3.32317 0.40 5.962689 −2.60892 0.405.480131 −1.89191 0.40 4.965835 −1.17948 0.40 4.416343 −0.48156 0.403.827652 0.189953 0.40 3.198752 0.823687 0.40 2.530092 1.407552 0.401.823085 1.927645 0.40 1.08222 2.370013 0.40 0.315583 2.721514 0.40−0.4645 2.972079 0.40 −1.24262 3.116774 0.40 −1.99979 3.157698 0.40−2.71937 3.103687 0.40 −3.38898 2.969239 0.40 −3.99804 2.77325 0.40−4.54239 2.534906 0.40 −5.02304 2.2751 0.40 −5.44416 2.011747 0.40−5.81242 1.760527 0.40 −6.13452 1.5333 0.40 −6.41701 1.339747 0.40−6.66564 1.188461 0.40 −6.8869 1.092479 0.40 −7.07862 1.067416 0.40−7.2204 1.109507 0.40 −7.30563 1.172752 0.40 −7.10518 1.808938 0.50−7.1315 1.854924 0.50 −7.16204 1.925516 0.50 −7.18909 2.041453 0.50−7.18794 2.206981 0.50 −7.13545 2.416526 0.50 −7.01766 2.659868 0.50−6.83197 2.927759 0.50 −6.57888 3.215462 0.50 −6.2588 3.518969 0.50−5.86991 3.831609 0.50 −5.41024 4.14419 0.50 −4.87902 4.446737 0.50−4.27609 4.726947 0.50 −3.60289 4.970225 0.50 −2.86266 5.158018 0.50−2.06118 5.266077 0.50 −1.21402 5.271481 0.50 −0.3365 5.153408 0.500.544762 4.90068 0.50 1.405912 4.514938 0.50 2.228771 4.009982 0.503.002867 3.405716 0.50 3.724091 2.722844 0.50 4.391774 1.979829 0.505.008183 1.193501 0.50 5.577186 0.378664 0.50 6.101745 −0.45279 0.506.584896 −1.2904 0.50 7.031562 −2.12387 0.50 7.445575 −2.94458 0.507.828356 −3.74586 0.50 8.182247 −4.52115 0.50 8.510119 −5.26429 0.508.812955 −5.9705 0.50 9.091478 −6.63562 0.50 9.347033 −7.25579 0.509.580125 −7.82807 0.50 9.790929 −8.35027 0.50 9.979851 −8.82073 0.5010.14719 −9.23853 0.50 10.29322 −9.6035 0.50 10.41833 −9.9162 0.5010.52312 −10.1779 0.50 10.60844 −10.3908 0.50 10.67444 −10.558 0.5010.68121 −10.6925 0.50 10.6459 −10.7794 0.50 10.60796 −10.8248 0.5010.57142 −10.8518 0.50 10.53405 −10.8688 0.50 10.48169 −10.8786 0.5010.39808 −10.8626 0.50 10.3074 −10.7835 0.50 10.23097 −10.6404 0.5010.138 −10.4555 0.50 10.02432 −10.2278 0.50 9.88927 −9.9554 0.509.732565 −9.63701 0.50 9.554231 −9.27196 0.50 9.354388 −8.86024 0.509.13336 −8.40244 0.50 8.891141 −7.89996 0.50 8.628114 −7.35456 0.508.344369 −6.76872 0.50 8.039625 −6.1456 0.50 7.713672 −5.48879 0.507.364905 −4.80305 0.50 6.992431 −4.09321 0.50 6.595427 −3.36455 0.506.17046 −2.62422 0.50 5.714973 −1.87958 0.50 5.227622 −1.13793 0.504.704592 −0.409 0.50 4.141513 0.295603 0.50 3.536843 0.964588 0.502.890565 1.586034 0.50 2.202816 2.145406 0.50 1.47601 2.62642 0.500.717317 3.013752 0.50 −0.06069 3.295736 0.50 −0.84135 3.46727 0.50−1.6043 3.530705 0.50 −2.33255 3.498526 0.50 −3.0132 3.386591 0.50−3.63559 3.213085 0.50 −4.19555 2.997266 0.50 −4.69248 2.757499 0.50−5.12878 2.510044 0.50 −5.50981 2.270435 0.50 −5.84194 2.050956 0.50−6.13204 1.86244 0.50 −6.38699 1.71546 0.50 −6.61307 1.624024 0.50−6.80723 1.604027 0.50 −6.94937 1.649699 0.50 −7.03339 1.716358 0.50−6.98039 1.79803 0.60 −7.00764 1.843232 0.60 −7.03919 1.91304 0.60−7.06795 2.028157 0.60 −7.06874 2.192811 0.60 −7.01724 2.402029 0.60−6.90134 2.645005 0.60 −6.71966 2.914105 0.60 −6.47248 3.204967 0.60−6.15907 3.512864 0.60 −5.77766 3.831325 0.60 −5.3273 4.153265 0.60−4.80583 4.467675 0.60 −4.21259 4.761933 0.60 −3.54795 5.01994 0.60−2.81481 5.222721 0.60 −2.0192 5.348978 0.60 −1.1757 5.377314 0.60−0.29817 5.289669 0.60 0.589433 5.075456 0.60 1.46511 4.733808 0.602.310537 4.275133 0.60 3.111118 3.712739 0.60 3.858774 3.064626 0.604.552564 2.351199 0.60 5.199768 1.595061 0.60 5.804196 0.810962 0.606.366353 0.009063 0.60 6.888339 −0.8005 0.60 7.374157 −1.60752 0.607.827039 −2.40337 0.60 8.24805 −3.18134 0.60 8.639261 −3.93479 0.609.002975 −4.65755 0.60 9.340417 −5.34459 0.60 9.65192 −5.99183 0.609.938039 −6.59564 0.60 10.19925 −7.15301 0.60 10.43564 −7.66174 0.6010.64755 −8.12014 0.60 10.83525 −8.52729 0.60 10.99899 −8.88299 0.6011.13923 −9.18777 0.60 11.25666 −9.44288 0.60 11.35222 −9.65035 0.6011.4257 −9.8137 0.60 11.43761 −9.94735 0.60 11.40692 −10.0356 0.6011.37179 −10.083 0.60 11.33705 −10.112 0.60 11.3007 −10.1311 0.6011.24894 −10.1438 0.60 11.16452 −10.1322 0.60 11.06955 −10.0581 0.6010.98569 −9.91916 0.60 10.88328 −9.73913 0.60 10.75798 −9.51743 0.6010.60905 −9.25216 0.60 10.43616 −8.94201 0.60 10.23926 −8.58634 0.6010.01861 −8.18508 0.60 9.774485 −7.73882 0.60 9.50697 −7.24895 0.609.216589 −6.71719 0.60 8.903715 −6.14592 0.60 8.56804 −5.53842 0.608.209379 −4.89838 0.60 7.827237 −4.23012 0.60 7.421186 −3.53838 0.606.989857 −2.8289 0.60 6.530746 −2.10862 0.60 6.041284 −1.3852 0.605.520111 −0.6662 0.60 4.96516 0.039485 0.60 4.374077 0.721583 0.603.743402 1.366894 0.60 3.070146 1.959479 0.60 2.354682 2.483548 0.601.601964 2.923995 0.60 0.822605 3.26914 0.60 0.030798 3.511077 0.60−0.75691 3.647199 0.60 −1.52211 3.682841 0.60 −2.24961 3.628923 0.60−2.92773 3.500147 0.60 −3.54659 3.313437 0.60 −4.10223 3.085928 0.60−4.59399 2.834939 0.60 −5.02489 2.577496 0.60 −5.40056 2.3289 0.60−5.72761 2.10147 0.60 −6.01209 1.904388 0.60 −6.26063 1.74719 0.60−6.48071 1.642508 0.60 −6.6733 1.60966 0.60 −6.81821 1.645478 0.60−6.90566 1.707748 0.60 −6.75158 2.268422 0.70 −6.77638 2.314422 0.70−6.80377 2.385148 0.70 −6.82458 2.500843 0.70 −6.81288 2.663147 0.70−6.74576 2.866066 0.70 −6.61312 3.097151 0.70 −6.41443 3.349923 0.70−6.15119 3.621323 0.70 −5.82607 3.911033 0.70 −5.43642 4.211884 0.70−4.97937 4.514812 0.70 −4.45291 4.808692 0.70 −3.85628 5.080711 0.70−3.19028 5.314806 0.70 −2.45825 5.4925 0.70 −1.66704 5.592566 0.70−0.83111 5.593401 0.70 0.034407 5.479193 0.70 0.906759 5.241346 0.701.765737 4.882631 0.70 2.594866 4.413829 0.70 3.382347 3.849565 0.704.118974 3.203683 0.70 4.803973 2.495405 0.70 5.441118 1.743484 0.706.034987 0.963499 0.70 6.586367 0.165769 0.70 7.097188 −0.63976 0.707.571516 −1.44294 0.70 8.012712 −2.2351 0.70 8.422021 −3.00953 0.708.802023 −3.75941 0.70 9.153814 −4.47926 0.70 9.482407 −5.16228 0.709.787257 −5.80492 0.70 10.06639 −6.40479 0.70 10.3211 −6.95856 0.7010.55141 −7.46404 0.70 10.75784 −7.91953 0.70 10.94055 −8.32413 0.7011.09957 −8.67778 0.70 11.23559 −8.98088 0.70 11.34946 −9.23459 0.7011.44206 −9.44095 0.70 11.5125 −9.60371 0.70 11.52107 −9.73637 0.7011.48968 −9.82328 0.70 11.45458 −9.87004 0.70 11.4201 −9.89866 0.7011.38392 −9.91768 0.70 11.33243 −9.93034 0.70 11.24839 −9.91889 0.7011.15389 −9.84508 0.70 11.07135 −9.70631 0.70 10.9711 −9.5262 0.7010.84848 −9.3044 0.70 10.70272 −9.03903 0.70 10.53359 −8.72877 0.7010.34084 −8.37305 0.70 10.12475 −7.9718 0.70 9.885691 −7.52557 0.709.623708 −7.03574 0.70 9.339322 −6.50405 0.70 9.032887 −5.93285 0.708.703944 −5.32546 0.70 8.351817 −4.68581 0.70 7.978269 −4.01692 0.707.582111 −3.3239 0.70 7.160786 −2.61304 0.70 6.711399 −1.89146 0.706.231205 −1.16686 0.70 5.718266 −0.44719 0.70 5.171185 0.259176 0.704.587229 0.941733 0.70 3.962514 1.586911 0.70 3.295134 2.179968 0.702.586022 2.705936 0.70 1.841443 3.15231 0.70 1.07142 3.508423 0.700.288748 3.766292 0.70 −0.49129 3.92263 0.70 −1.25182 3.97941 0.70−1.97695 3.946674 0.70 −2.65527 3.837804 0.70 −3.27604 3.66888 0.70−3.83525 3.458211 0.70 −4.33219 3.223701 0.70 −4.76966 2.982483 0.70−5.1524 2.749057 0.70 −5.48695 2.536327 0.70 −5.77971 2.354933 0.70−6.0347 2.211141 0.70 −6.25764 2.115759 0.70 −6.44909 2.08081 0.70−6.59381 2.11345 0.70 −6.68048 2.176013 0.70 −6.65242 2.910788 0.80−6.67481 2.957722 0.80 −6.70046 3.028752 0.80 −6.72602 3.142701 0.80−6.73084 3.305032 0.80 −6.68813 3.512604 0.80 −6.57392 3.751986 0.80−6.3797 4.006305 0.80 −6.1114 4.270088 0.80 −5.76846 4.534413 0.80−5.35313 4.793894 0.80 −4.86911 5.046017 0.80 −4.31925 5.286373 0.80−3.70536 5.507517 0.80 −3.02897 5.697076 0.80 −2.29315 5.84004 0.80−1.50376 5.918422 0.80 −0.67169 5.912648 0.80 0.190127 5.803856 0.801.060977 5.57822 0.80 1.919778 5.231658 0.80 2.748413 4.772037 0.803.53382 4.213341 0.80 4.270348 3.574753 0.80 4.956992 2.874936 0.805.594842 2.130116 0.80 6.187224 1.355181 0.80 6.735292 0.561079 0.807.242028 −0.24136 0.80 7.711406 −1.042 0.80 8.146658 −1.83225 0.808.549318 −2.60519 0.80 8.921881 −3.35407 0.80 9.267239 −4.07257 0.809.584205 −4.75687 0.80 9.874924 −5.4021 0.80 10.14173 −6.00392 0.8010.38477 −6.55955 0.80 10.60434 −7.06675 0.80 10.8009 −7.52385 0.8010.97485 −7.92987 0.80 11.12654 −8.28461 0.80 11.25639 −8.58858 0.8011.36505 −8.84305 0.80 11.45333 −9.05006 0.80 11.51965 −9.21358 0.8011.52568 −9.34568 0.80 11.49343 −9.43166 0.80 11.45773 −9.47767 0.8011.42282 −9.50539 0.80 11.3862 −9.52336 0.80 11.33451 −9.53428 0.8011.25099 −9.51986 0.80 11.15854 −9.44407 0.80 11.07838 −9.30443 0.8010.98207 −9.12279 0.80 10.86429 −8.89914 0.80 10.72429 −8.63158 0.8010.56179 −8.31882 0.80 10.37674 −7.96022 0.80 10.16947 −7.55568 0.809.940002 −7.10593 0.80 9.688295 −6.61237 0.80 9.4149 −6.07671 0.809.119922 −5.5014 0.80 8.802762 −4.8898 0.80 8.463367 −4.24546 0.808.099988 −3.57326 0.80 7.709609 −2.87934 0.80 7.293141 −2.16813 0.806.847855 −1.44662 0.80 6.370769 −0.72269 0.80 5.859938 −0.00435 0.805.31186 0.698263 0.80 4.724304 1.374516 0.80 4.095379 2.012221 0.803.42467 2.598053 0.80 2.713665 3.117358 0.80 1.966949 3.555129 0.801.194378 3.899967 0.80 0.409746 4.144698 0.80 −0.37074 4.288163 0.80−1.12975 4.334071 0.80 −1.85269 4.291255 0.80 −2.52765 4.174246 0.80−3.14553 4.001281 0.80 −3.70339 3.79171 0.80 −4.20151 3.56341 0.80−4.64326 3.333222 0.80 −5.03363 3.11513 0.80 −5.37905 2.922625 0.80−5.68591 2.768787 0.80 −5.95913 2.665858 0.80 −6.19886 2.630535 0.80−6.39021 2.658433 0.80 −6.51803 2.734264 0.80 −6.5906 2.812167 0.80−6.47299 3.641768 0.90 −6.49137 3.689349 0.90 −6.51206 3.760485 0.90−6.53306 3.873066 0.90 −6.5366 4.032292 0.90 −6.4969 4.236309 0.90−6.38581 4.471474 0.90 −6.18997 4.716806 0.90 −5.91325 4.960791 0.90−5.56171 5.198707 0.90 −5.14008 5.428236 0.90 −4.65145 5.645851 0.90−4.09823 5.84618 0.90 −3.48314 6.022606 0.90 −2.80939 6.166548 0.90−2.08102 6.266807 0.90 −1.30418 6.30898 0.90 −0.48809 6.276168 0.900.354935 6.153111 0.90 1.208051 5.927258 0.90 2.052766 5.5935 0.902.872038 5.155114 0.90 3.654138 4.624382 0.90 4.392136 4.016684 0.905.082536 3.347439 0.90 5.725526 2.632229 0.90 6.321819 1.884114 0.906.873279 1.115017 0.90 7.382797 0.33597 0.90 7.854262 −0.44275 0.908.290135 −1.21288 0.90 8.692345 −1.96721 0.90 9.063787 −2.69874 0.909.406733 −3.40145 0.90 9.722287 −4.07047 0.90 10.01166 −4.70144 0.9010.2762 −5.29047 0.90 10.51651 −5.83463 0.90 10.73308 −6.3316 0.9010.92657 −6.77965 0.90 11.09747 −7.17778 0.90 11.24618 −7.52576 0.9011.37331 −7.82402 0.90 11.47959 −8.07374 0.90 11.56574 −8.27697 0.9011.62919 −8.43799 0.90 11.63269 −8.56768 0.90 11.60032 −8.65175 0.9011.56508 −8.6967 0.90 11.53074 −8.72377 0.90 11.49464 −8.74138 0.9011.44371 −8.75207 0.90 11.36141 −8.73824 0.90 11.26925 −8.66487 0.9011.18957 −8.52785 0.90 11.09503 −8.34879 0.90 10.97932 −8.12835 0.9010.84165 −7.86472 0.90 10.6817 −7.55663 0.90 10.4993 −7.20352 0.9010.29457 −6.80539 0.90 10.06731 −6.36306 0.90 9.81777 −5.8778 0.909.546049 −5.35147 0.90 9.251904 −4.78672 0.90 8.93467 −4.1869 0.908.593791 −3.5558 0.90 8.228447 −2.89784 0.90 7.837048 −2.21833 0.907.41783 −1.52321 0.90 6.968695 −0.81922 0.90 6.486855 −0.11424 0.905.96978 0.58311 0.90 5.414599 1.262799 0.90 4.819474 1.914099 0.904.183257 2.525023 0.90 3.506679 3.083003 0.90 2.792893 3.57532 0.902.047813 3.989589 0.90 1.280489 4.314459 0.90 0.503528 4.540975 0.90−0.26753 4.663007 0.90 −1.01491 4.685997 0.90 −1.72527 4.622874 0.90−2.38663 4.493472 0.90 −2.99428 4.320001 0.90 −3.54674 4.121816 0.90−4.04549 3.915809 0.90 −4.49348 3.71571 0.90 −4.89487 3.534287 0.90−5.25441 3.384148 0.90 −5.5751 3.277805 0.90 −5.85882 3.225967 0.90−6.09511 3.253514 0.90 −6.26121 3.347833 0.90 −6.36347 3.452049 0.90−6.42222 3.538935 0.90 −6.39565 4.13931 1.00 −6.41156 4.185778 1.00−6.42789 4.25532 1.00 −6.43869 4.364959 1.00 −6.4238 4.517393 1.00−6.35723 4.706621 1.00 −6.21597 4.913516 1.00 −5.99672 5.121641 1.00−5.70457 5.323747 1.00 −5.34442 5.517192 1.00 −4.92012 5.700913 1.00−4.434 5.87152 1.00 −3.88804 6.023454 1.00 −3.28484 6.150136 1.00−2.62802 6.245387 1.00 −1.92231 6.303105 1.00 −1.17306 6.317121 1.00−0.38696 6.280227 1.00 0.427978 6.183683 1.00 1.260305 6.012003 1.002.095284 5.751723 1.00 2.915397 5.393559 1.00 3.706025 4.942248 1.004.458175 4.411021 1.00 5.166851 3.814708 1.00 5.830771 3.168652 1.006.450347 2.48658 1.00 7.02752 1.781124 1.00 7.565155 1.063679 1.008.065635 0.343813 1.00 8.530543 −0.37049 1.00 8.962146 −1.07163 1.009.363025 −1.75258 1.00 9.734805 −2.40753 1.00 10.07853 −3.03157 1.0010.39499 −3.62051 1.00 10.68505 −4.17065 1.00 10.94889 −4.67922 1.0011.18681 −5.144 1.00 11.3995 −5.56319 1.00 11.58703 −5.93597 1.0011.74943 −6.26227 1.00 11.88799 −6.54212 1.00 12.00376 −6.77648 1.0012.09726 −6.96742 1.00 12.16451 −7.11995 1.00 12.17133 −7.24492 1.0012.14308 −7.32725 1.00 12.11125 −7.37195 1.00 12.07952 −7.39964 1.0012.04548 −7.41853 1.00 11.99671 −7.43163 1.00 11.9164 −7.42333 1.0011.82078 −7.36033 1.00 11.73468 −7.23287 1.00 11.6336 −7.06461 1.0011.50972 −6.85747 1.00 11.36207 −6.60981 1.00 11.19035 −6.3204 1.0010.99381 −5.98899 1.00 10.77232 −5.61575 1.00 10.52612 −5.20125 1.0010.25579 −4.74654 1.00 9.961139 −4.25366 1.00 9.642481 −3.72496 1.009.299377 −3.1637 1.00 8.931688 −2.5735 1.00 8.53898 −1.9586 1.008.118825 −1.32505 1.00 7.669639 −0.67892 1.00 7.190178 −0.02667 1.006.678205 0.623794 1.00 6.131296 1.263427 1.00 5.547074 1.881889 1.004.924346 2.468192 1.00 4.262233 3.00932 1.00 3.562026 3.491522 1.002.828837 3.90256 1.00 2.07136 4.232821 1.00 1.301833 4.478196 1.000.533937 4.639737 1.00 −0.21891 4.722939 1.00 −0.94509 4.737683 1.00−1.63553 4.696473 1.00 −2.28411 4.613892 1.00 −2.88697 4.504207 1.00−3.44219 4.379261 1.00 −3.94862 4.247692 1.00 −4.40654 4.118804 1.00−4.8169 4.000773 1.00 −5.18113 3.901274 1.00 −5.50082 3.827008 1.00−5.77753 3.790627 1.00 −6.00805 3.798574 1.00 −6.1813 3.864184 1.00−6.28894 3.956253 1.00 −6.34811 4.038869 1.00 −5.88703 5.165532 1.08−5.89637 5.212294 1.08 −5.90255 5.281373 1.08 −5.89529 5.387798 1.08−5.85253 5.530437 1.08 −5.75064 5.696659 1.08 −5.57226 5.861917 1.08−5.32184 6.014664 1.08 −5.00488 6.150653 1.08 −4.62605 6.26912 1.08−4.1885 6.369487 1.08 −3.6946 6.448516 1.08 −3.1469 6.500853 1.08−2.54898 6.521558 1.08 −1.90504 6.505786 1.08 −1.21994 6.449872 1.08−0.4992 6.351684 1.08 0.25137 6.209256 1.08 1.0253 6.02001 1.08 1.8135715.775863 1.08 2.603679 5.464671 1.08 3.380669 5.07619 1.08 4.1307064.609059 1.08 4.843865 4.070299 1.08 5.513786 3.470777 1.08 6.1384672.82396 1.08 6.717509 2.142233 1.08 7.253389 1.438212 1.08 7.7491870.722985 1.08 8.206687 0.00536 1.08 8.62835 −0.70641 1.08 9.016984−1.40476 1.08 9.375524 −2.08283 1.08 9.705275 −2.73526 1.08 10.00665−3.3577 1.08 10.28217 −3.94529 1.08 10.53314 −4.49434 1.08 10.76016−5.00204 1.08 10.96402 −5.46607 1.08 11.14537 −5.88476 1.08 11.30535−6.2569 1.08 11.44455 −6.58215 1.08 11.56336 −6.86102 1.08 11.66243−7.09462 1.08 11.74193 −7.28505 1.08 11.79633 −7.43747 1.08 11.79329−7.55888 1.08 11.75967 −7.63665 1.08 11.72595 −7.67774 1.08 11.69352−7.70264 1.08 11.6593 −7.71913 1.08 11.61102 −7.72942 1.08 11.5332−7.71797 1.08 11.44152 −7.65354 1.08 11.3636 −7.52503 1.08 11.27475−7.35524 1.08 11.16587 −7.14624 1.08 11.03607 −6.89643 1.08 10.88482−6.60473 1.08 10.71204 −6.27055 1.08 10.51756 −5.89405 1.08 10.30143−5.47589 1.08 10.0631 −5.01765 1.08 9.802362 −4.52129 1.08 9.518987−3.98933 1.08 9.211926 −3.4252 1.08 8.88037 −2.83271 1.08 8.523807−2.216 1.08 8.13985 −1.58077 1.08 7.726565 −0.93304 1.08 7.281962−0.27954 1.08 6.804118 0.372304 1.08 6.289753 1.013098 1.08 5.7363071.632571 1.08 5.142628 2.219882 1.08 4.509026 2.763558 1.08 3.8368893.250631 1.08 3.132411 3.671609 1.08 2.405162 4.021046 1.08 1.6675564.300243 1.08 0.932349 4.516295 1.08 0.210106 4.676338 1.08 −0.490464.787629 1.08 −1.16221 4.858334 1.08 −1.79941 4.896726 1.08 −2.397554.910454 1.08 −2.95318 4.906086 1.08 −3.46383 4.888881 1.08 −3.927694.864618 1.08 −4.34378 4.838495 1.08 −4.71178 4.816713 1.08 −5.031854.80407 1.08 −5.30425 4.805224 1.08 −5.52897 4.823677 1.08 −5.698994.884573 1.08 −5.80132 4.977733 1.08 −5.85221 5.062824 1.08 −5.781125.670107 1.15 −5.78804 5.716156 1.15 −5.79044 5.78369 1.15 −5.775665.88671 1.15 −5.72016 6.021252 1.15 −5.6029 6.171674 1.15 −5.409996.309628 1.15 −5.14931 6.427472 1.15 −4.8273 6.525173 1.15 −4.447496.601776 1.15 −4.0127 6.65661 1.15 −3.52552 6.686809 1.15 −2.988636.689376 1.15 −2.40553 6.658488 1.15 −1.78058 6.590308 1.15 −1.118236.484389 1.15 −0.4232 6.340133 1.15 0.300563 6.161131 1.15 1.04825.947322 1.15 1.813376 5.695599 1.15 2.586701 5.397054 1.15 3.3559595.040441 1.15 4.107202 4.617027 1.15 4.82923 4.127669 1.15 5.5134673.578557 1.15 6.156035 2.980925 1.15 6.754644 2.345656 1.15 7.3112351.685574 1.15 7.828428 1.011927 1.15 8.306924 0.333075 1.15 8.748369−0.3429 1.15 9.156092 −1.00779 1.15 9.532384 −1.65487 1.15 9.878431−2.27874 1.15 10.19559 −2.87448 1.15 10.48553 −3.43755 1.15 10.74956−3.96422 1.15 10.98822 −4.45168 1.15 11.20236 −4.89753 1.15 11.39287−5.30001 1.15 11.56045 −5.65803 1.15 11.70561 −5.9713 1.15 11.82926−6.24004 1.15 11.93232 −6.46519 1.15 12.01491 −6.64889 1.15 12.07064−6.79655 1.15 12.06714 −6.91523 1.15 12.03541 −6.9915 1.15 12.00342−7.03235 1.15 11.9725 −7.05755 1.15 11.93943 −7.07487 1.15 11.89241−7.08673 1.15 11.81556 −7.07883 1.15 11.72248 −7.02005 1.15 11.64137−6.89675 1.15 11.54961 −6.73234 1.15 11.43702 −6.53003 1.15 11.30268−6.28825 1.15 11.14589 −6.00604 1.15 10.9663 −5.68299 1.15 10.76364−5.31929 1.15 10.53776 −4.91572 1.15 10.28822 −4.47384 1.15 10.01494−3.99554 1.15 9.717556 −3.48344 1.15 9.394854 −2.94114 1.15 9.045985−2.37257 1.15 8.670623 −1.78183 1.15 8.266454 −1.1748 1.15 7.830951−0.55819 1.15 7.363772 0.06214 1.15 6.862412 0.677939 1.15 6.3235141.279061 1.15 5.745414 1.855162 1.15 5.129065 2.396731 1.15 4.4750082.891762 1.15 3.786505 3.328839 1.15 3.071926 3.702324 1.15 2.3422834.012217 1.15 1.610475 4.267095 1.15 0.887676 4.478065 1.15 0.1824134.654047 1.15 −0.49869 4.802137 1.15 −1.15073 4.925947 1.15 −1.769585.028039 1.15 −2.35163 5.110622 1.15 −2.89392 5.174226 1.15 −3.393955.217864 1.15 −3.84932 5.24136 1.15 −4.25791 5.246803 1.15 −4.619065.242396 1.15 −4.93456 5.239273 1.15 −5.20748 5.25498 1.15 −5.434795.304685 1.15 −5.601 5.388146 1.15 −5.70105 5.483858 1.15 −5.750035.568248 1.15 −5.7713 5.627714 1.15

In the above table, the plane Zadim=0 corresponds to the reference planeP0 situated at the base of the profile. This plane P0 is theintersection of the stacking axis AE of the set of blades with theaxisym metric surface of the hub, i.e. it passes via the intersectionbetween the axis AE and the surface where it is assembled with theplatform 14. The plane Zadim=1 corresponds to the reference plane P1situated at the top of the profile. This plane P1 is the intersectionbetween the axis AE and the axisym metric surface of the casing, i.e. itpasses via the intersection of the axis AE with the surface where it isassembled with the top platform 10.

By convention, the stacking axis AE of a blade of a rotary wheel, is anaxis that extends in the radial direction Z and is an axis on which thevarious X,Y sections of the set of blades are “stacked” when designingthe set of blades.

As mentioned at the beginning of the present description, theaerodynamic profile of the disclosure is substantially identical to thenominal profile defined in the above table, i.e. it departs from saidnominal profile by very little at most, being defined in particularwithin an envelope of ±1 mm in a direction normal to the surface of thenominal profile, and/or having X,Y coordinates lying within a range of±5% relative to the coordinates X,Y of the nominal profile. Also, theaerodynamic profile is positioned rotated within ±10°, particularlywithin ±5°, more particularly within ±3°, with respect to the stackingaxis of the blade. In other words, the stagger angle may vary by ±10°,particularly by ±5°, more particularly by ±3°.

The coordinates of the above table are given starting from a valueZadim=0 in the reference plane P0. The coordinate Zadim isnon-dimensional, i.e. for a point P, situated at a distance D from theplane P0 (where D is measured along the axis Z), the value of Zadim isD/H, where H represents the total height of the profile as measuredbetween the planes P0 and P1. Naturally, in the table above, bymultiplying the coordinate Zadim by the height H, it is possible toobtain the complete coordinates of the blade.

Preferably, the height H of the profile of the blade lies in the range65 mm±10%. By way of example, the reference plane P0 is at a distance ofabout 433 mm±10% from the axis A of the turbine.

In the above table, the profile is characterized by fifteen sectionplanes at constant Zadim coordinates, for which the coordinates X and Yare specified. These fifteen section planes include eleven sectionplanes located between Zadim=0 and Zadim=1, and thus arranged in thefluid stream, these section planes being distributed on the vane'sheight from P0 to P1. The fifteen section planes also include foursection planes which are substantially outside the fluid stream (twosection planes with Zadim<0, and two section planes with Zadim>1), thesefour section planes being provided for ensuring geometric continuity ofthe stacking, close to the head and the foot, respectively. In eachsection plane at constant coordinate Zadim, the section of the profileis given by a continuous and smooth curve, interconnecting all of thepoints (X,Y). In each section plane, the profile is interpolated so asto generate a uniform profile.

It is advantageous for the rotary wheel that includes the blade of thedisclosure to have 147 to 167 blades, in particular 157 blades, thatpresent aerodynamic profiles as defined above.

We claim:
 1. An aerodynamic profile for a turbine blade, the profilebeing, when cold and in a non-coated state, substantially identical to anominal profile determined by the Cartesian coordinates X,Y,Zadim givenin Table 1, in which the coordinate Zadim is the quotient D/H, where Dis the distance of the point under consideration from a first referenceX,Y plane situated at the base of the nominal profile, and H is theheight of said profile measured from said first reference plane that isthe intersection of the stacking axis of the blade and the axisymmetricsurface of the hub, out to a second reference plane that is theintersection of said stacking axis with the axisymmetric surface of thecasing, the measurements D and H being taken radially relative to theaxis of the turbine, while the coordinate X is measured in the axialdirection of the turbine.
 2. The aerodynamic profile as claimed in claim1, wherein said profile is defined within an envelope of ±1 mm in adirection normal to the surface of the nominal profile.
 3. Theaerodynamic profile as claimed in claim 1, wherein the coordinates X,Yof said profile lie within a range of ±5% relative to the coordinatesX,Y of the nominal profile.
 4. The aerodynamic profile as claimed inclaim 1, wherein the aerodynamic profile may be positioned rotatedwithin ±10° with respect to the stacking axis of the blade.
 5. Theaerodynamic profile as claimed in claim 1, wherein the aerodynamicprofile may be positioned rotated within ±5° with respect to thestacking axis of the blade.
 6. The aerodynamic profile as claimed inclaim 1, wherein the aerodynamic profile may be positioned rotatedwithin ±3° with respect to the stacking axis of the blade.
 7. Theaerodynamic profile as claimed in claim 1, wherein the blade is a bladeof a rotary wheel forming a portion of a rotor of a turbine.
 8. Aturbine blade, presenting the aerodynamic profile as claimed in claim 1.9. A turbine, including turbine blades presenting aerodynamic profilesas claimed in claim
 1. 10. A turbine as claimed in claim 9, including arotary wheel, having 147 to 167 blades that present the aerodynamicprofiles.
 11. A turbine as claimed in claim 9, including a rotary wheel,having 157 blades that present the aerodynamic profiles.
 12. A rotarywheel of a turbine forming a portion of a turbine rotor, wherein all theblades of this rotary wheel present an aerodynamic profile as claimed inclaim
 1. 13. The rotary wheel of a turbine as claimed in claim 12,including 147 to 167 blades that present the aerodynamic profiles. 14.The rotary wheel of a turbine as claimed in claim 12, including 157blades that present the aerodynamic profiles.